What does the "Camera Clip" checkbox do in the "Background Images", "Movie Clip" tab do?
The Camera Clip option is referring to the active movie clip for the scene. This would normally be the clip that you are using for camera tracking.

In the scene properties you will find the setting for Active Clip. This active clip for the scene is the one referred to by the Camera Clip setting. The available clips are the clips that have been loaded into the movie clip editor for camera/object tracking.



While the same clip can be chosen in the background settings, by using the scene's active clip you can use the same setting in multiple views and change them all in one place.